We investigate the influence of different spin-orbit couplings on topological phase transitions in the bilayer Kane-Mele model. We find that the competition between intrinsic spin-orbit coupling and Rashba spin-orbit coupling can lead to two dimensional topological metallic states with nontrivial topology. Such phases, although having a metallic bulk, still possess edge states with well-defined topological invariants. Specifically, we show that with preserved time reversal symmetry, the system can exhibit a Z2-metallic phase with spin helical edge states and a nontrivial Z2 invariant. When time reversal symmetry is broken, a Chern metallic phase could appear with chiral edge states and a nontrivial Chern invariant.
@article{arxiv.1402.6502,
title = {Topological metallic states in spin-orbit coupled bilayer systems},
author = {Hui Pan and Xin Li and Zhenhua Qiao and Cheng-Cheng Liu and Yugui Yao and Shengyuan A. Yang},
journal= {arXiv preprint arXiv:1402.6502},
year = {2014}
}